M2-branes and plane partitions

Abstract

There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry ℂ2 probed by a stack of N M2-branes and plane partitions of trace N. We give combinatorial expressions of the indices which count the local operators parametrizing ℂ2/ℤk probed by N M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. We derive the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large N limit.

Dualities and flavored indices of M2-brane SCFTs

“…The asymptotic behavior of the degeneracy of the states has attracted significant attention in conformal field theories [1][2][3][4][5], superconformal field theories (SCFTs) [6][7][8][9][10][11][12], the T T deformed theories [13][14][15], effective field theories [16,17] and quantum field theories with a finite group global symmetry [18][19][20]. In particular, the superconformal field theories which have holographically dual descriptions are expected to capture the state densities of p-branes in string theory/M-theory as well as the BPS black holes.…”

$$ \mathcal{N} $$ = 2* Schur indices

“…3 See [42,43] for the combinatorial interpretations for supersymmetric indices of M2-brane SCFTs. 4 See [47] for the analysis of the unflavored Schur indices.…”

Exact stringy microstates from gauge theories

“…1 Though the problem of counting degeneracies can be studied in gauge theory, a bulk understanding of string theory microstates has been absent. Clues regarding the structure of these bulk microstates have come from recent works [42,43] (see also [44][45][46][47][48][49][50][51][52][53][54]) that found a reorganization of finite N superconformal indices in terms of branes and their excitations in the string dual. In the work [42] with D. Gaiotto, we proposed a brane expansion of the superconformal index by counting branes and their excitations via determinant operators in gauge theory.…”